m e m o l i @ m a t h . s t a n f o r d . e d u

Publications

Manuscripts in preparation and preprints

• Some properties of Gromov-Hausdorff distances. F. Mémoli. [submitted].
• Classifying Clustering Schemes. G. Carlsson and F. Mémoli. November 2010, Arxiv. [submitted].
• Local scales of embedded curves and surfaces. T.M. Le and F. Mémoli. [in preparation].
• Topological stability of the hippocampal spatial map. Yuri Dabaghian, F. Mémoli,Gunnar Carlsson and Loren Frank. [in preparation] [ Poster presented SfN-2010].
• Gromov-Hausdorff and Gromov-Wasserstein distances in Euclidean spaces. F. Mémoli. [in preparation].
• Gromov-Wasserstein distances for Partial Shape Matching. F. Mémoli. [in preparation].
• Local Scale Selection for Exploratory Visualization and Analysis of Massive Datasets. G.Carlsson, F.Mémoli and G.Singh. [preprint-- March 2009].
• On a connection between the use of Persistence Topology for shape matching and the Gromov-Haudorff distance. F. Mémoli. [preprint-- July 2008].
• Persistent Clustering and a Theorem of J. Kleinberg. G. Carlsson and F. Mémoli. August 2008, Arxiv.

Journal, conference, and workshop

• Gromov-Wasserstein distances and the metric approach to object matching. F. Mémoli. Foundations of Computational Mathematics. April 29, 2011. [BibTex]
• A spectral notion of Gromov-Wasserstein distances and related methods. F. Mémoli. Journal of Applied and Computational Harmonic Analysis 30 (2011), pp.363-401. [BibTex]
• One Point Isometric Matching with the Heat Kernel With M. Ovsjanikov, Q. Mérigot, and L. Guibas. Proc. Eurographics Symposium on Geometry Processing (SGP) 2010. [BibTex].
• Characterization, stability and convergence of hierarchical clustering algorithms. G.Carlsson and F.Mémoli. JMLR, 11(Apr):1425--1470, 2010. [BibTex].
• Some ideas for formalizing clustering schemes. G.Carlsson and F.Mémoli. NIPS 2009 workshop "Clustering: science or art?" . See talks section for the talk materials.
• Multiparameter clustering algorithms. G.Carlsson and F.Mémoli. IFCS 2009. [BibTex].
• Spectral Gromov-Wasserstein distances for shape matching NORDIA-ICCV-2009. [BibTex].
• Gromov-Hausdorff stable signatures for shapes using persistence, with F. Chazal, D. Cohen-Steiner, S. Oudot and L. Guibas. SGP-2009. [BibTex]
• Gromov-Hausdorff distances in Euclidean spaces. F. Mémoli. NORDIA-CVPR-2008. [BibTex].
• Stability of clustering methods with Gunnar Carlsson. Mathematisches Forschungsinstitut Oberwolfach Report No. 29/2008, "Computational Algebraic Topology". [BibTex].
• Topological Analysis of Population Activity in Primary Visual Cortex. G. Singh, F. Mémoli, T. Ishkhanov, G. Carlsson, G. Sapiro and D. Ringach. Jounal of Vision, Volume 8, Number 8, Article 11, Pages 1-18. [preprint version is linked here, see the publisher's site for the journal version].[BibTex].
• On the Use of Gromov-Hausdorff Distances for Shape Comparison. F. Mémoli. Symposium on Point Based Graphics 2007, Prague, September 2007. [BibTex].
• Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. G. Singh, F. Mémoli and G. Carlsson. Symposium on Point Based Graphics 2007, Prague, September 2007. [BibTex].
• Meshless Geometric Subdivision. Facundo Mémoli, Carsten Moenning, Guillermo Sapiro, Nira Dyn and Neil Dodgson. Graphical Models Volume 69, Issues 3-4, May-July 2007, Pages 160-179. [BibTex].
• Brain and surface warping via minimizing Lipschitz extensions. Facundo Mémoli, Guillermo Sapiro, and Paul Thompson. MFCA-2006 International Workshop on Mathematical Foundations of Computational Anatomy. MICCAI. [BibTex].
• A theoretical and computational framework for isometry invariant recognition of point cloud data. Facundo Mémoli and Guillermo Sapiro. Found. Comput. Math. 5 (2005), no. 3, 313--347. [BibTex]
• Comparing Point Clouds. Facundo Mémoli and Guillermo Sapiro. SGP 2004 . [BibTex].
• Implicit Brain Imaging. Facundo Mémoli, G. Sapiro and P.M. Thompson. (2004). NeuroImage, Special Issue on Mathematics in Brain Imaging, Thompson, P.M., Miller, M.I., Ratnanather, J.T., Poldrack, R., Nichols, T.E., [eds.]. [BibTex].
• Distance functions and geodesics on submanifolds of ${\Bbb R}\sp d$ and point clouds. Facundo Mémoli and Guillermo Sapiro. SIAM J. Appl. Math. 65 (2005), no. 4, 1227--1260. [BibTex].
• Solving variational problems and partial differential equations mapping into general target manifolds. Facundo Mémoli, Guillermo Sapiro and Stanley Osher. J. Comput. Phys. 195 (2004), no. 1, 263--292. [BibTex].
• Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces. Facundo Mémoli and Guillermo Sapiro. J. Comput. Phys. 173 (2001), no. 2, 730--764. [BibTex].

Book chapters

• Variational problems and partial differential equations on implicit surfaces: bye bye triangulated surfaces? Mémoli, Facundo; Bertalmio, Marcelo; Cheng, Li-Tien; Sapiro, Guillermo; Osher, Stanley Variational problems and partial differential equations on implicit surfaces: bye bye triangulated surfaces? Geometric level set methods in imaging, vision, and graphics, 381--397, Springer, New York, 2003. [BibTex].
• Computing with Point Cloud Data. Mémoli, Facundo; Sapiro, Guillermo. Statistics and Analysis of Shapes (Modeling and Simulation in Science, Engineering and Technology). Birkhauser; 1 edition (May 3, 2006). [BibTex].

Theses

• PhD Thesis

  "Estimation Of Distance Functions And Geodesics And Its Use For Shape Comparison And Alignment: Theoretical And Computational Results." University of Minnesota, May 2005. [BibTex]

• MSci. Thesis

  Distance Maps on Implicitly Defined Manifolds. Universidad de la Rep\'ublica. Uruguay, 2001. [BibTex]

Software

• Flujos . Software for Curve and Surface evolution.